Skip to main content
SpringerLink
Log in
Book cover

Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

  • Textbook
  • © 2006

Overview

Authors:
  1. Jürgen Jost

    1. Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory
  • The analytic approach is likewise new as it is based on the theory of harmonic maps
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages I-XVIII
    Download chapter PDF

  2. Topological Foundations

    Pages 1-16

  3. Differential Geometry of Riemann Surfaces

    Pages 17-78

  4. Harmonic Maps

    Pages 79-159

  5. Teichmüller Spaces

    Pages 161-186

  6. Geometric Structures on Riemann Surfaces

    Pages 187-265

  7. Erratum to: Characterizing Programming Systems Allowing Program Self-reference

    • John Case, Samuel E. Moelius
    Pages 266-266

  8. Back Matter

    Pages 267-281
    Download chapter PDF
Back to top

Keywords

About this book

Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Reviews

From the reviews:

"Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost’s explicit dictum that there are three foci around which the whole subject revolves … . Jost’s presentation is quite accessible, modulo a lot of diligence on the part of the reader. It’s a very good and useful book, very well-written and thorough." (Michael Berg, MathDL, April, 2007)

From the reviews of the third edition:

“Geometrical facts about Riemann surfaces are as ‘nice’ as possible, and they often provide the intuition and motivation for generalizations to other curves, manifolds or varieties. The Riemann–Roch theorem … is a prime example of this influence. This book is amazing, very well written, accessible and works as a first course on Riemannian Surfaces I recommend to the all readers interested in Geometry and Riemannian Geometry.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)

Authors and Affiliations

  • Max Planck Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Jürgen Jost

Bibliographic Information

  • Book Title: Compact Riemann Surfaces

  • Book Subtitle: An Introduction to Contemporary Mathematics

  • Authors: Jürgen Jost

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-540-33067-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Softcover ISBN: 978-3-540-33065-3Published: 19 June 2006

  • eBook ISBN: 978-3-540-33067-7Published: 13 December 2006

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 3

  • Number of Pages: XVIII, 282

  • Number of Illustrations: 23 b/w illustrations

  • Topics: Differential Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation